The endorsement of the legislation counters the view of many other insurers

Anthem Inc. said it believes that the Senate Republicans’ health bill will bolster the individual insurance market, an endorsement for the legislation as many other insurers have suggested it could undermine the marketplaces created by the Affordable Care Act.

In a statement, Anthem said it believed the bill “will markedly improve the stability of the individual market and moderate premium increases,” because it allots billions to...